Answer:the width of plywood = 6.25 feet wide or 6 1/4 feet wide
Step-by-step explanation:
Step 1
Area of a rectangular plywood = length x width
Area of Ist Plywood= 7 x w
Area of 2nd Plywood= 61/2 x w=6.5 xw
But Total Arae of trhe two Plywoods are = 84 3/8 square feet.
Therefore Our equation to solve the problem becomes
Area of Ist Plywood + Area of 2nd Plywood =84 3/8 square feet.
7w + 6.5w = 84 3/8
13.5w= 84 3/8
w = 84 3/8/13.5
675/8 / 13.5
w=6.25
Therefore the width of plywood = 6.25 feet wide or 6 1/4 feet.
So some quick tips for inequalities:
**What you do to one side you HAVE TO do it to the other 2**
**If you ever divide a negative number past the inequality signs, the signs FLIP!!**
(e.g. 2>-5x>25)
-2/5 <x < -5
I hope that this has helped!
Answer:
a) Y(x) = {900, x≤30; 900-40(x-30), x>30}
b) T(x) = {900x, x≤30; 2100x-40x², x>30}
c) dT/dx = {900, x≤30; 2100-80x, x>30}
Step-by-step explanation:
a) The problem statement gives the function for x ≤ 30, and gives an example of evaluating the function for x = 35. So, replacing 35 in the example with x gives the function definition for x > 30.

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b) The yield per acre is the product of the number of trees and the yield per tree:
T(x) = x·Y(x)

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c) The derivative is ...

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The attached graph shows the yield per acre (purple, overlaid by red for x<30), the total yield (black), and the derivative of the total yield (red). You will note the discontinuity in the derivative at x=30, where adding one more tree per acre suddenly makes the rate of change of yield be negative.